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Matrix Commands
in Excel
Anthony Murphy
Nuffield College
[email protected]
Matrix Commands in Excel
Excel can perform some useful, albeit basic, matrix
operations:
• Addition & subtraction;
• Scalar multiplication & division;
• Transpose (TRANSPOSE);
• Matrix multiplication (MMULT);
• Matrix inverse (MINVERSE);
• Determinant of matrix (MDETERM);
As well as combinations of these operations.
Matrix Commands in Excel (Cont’d)
• In Excel the matrix commands (and some
other commands) are called ARRAY
commands.
• Can perform more complicated operations
using free add-ins for Excel e.g. MATRIX.
• Alternatively, can use matrix package like
MATLAB (which also does symbolic maths
& matrix algebra).
Excel (Cont’d)
• The matrix commands in Excel are
sufficient for this course.
• If you are really keen, you can play around
with Visual Basic for Applications (VBA),
the Excel programming language.
• For example, see Benninga, S. (2000),
Financial Modelling, MIT Press.
Named Cells
• Most Excel formulae require you to name one or
more cell ranges e.g. b2.c4.
• You can type these in directly or select them
using the mouse.
• However, it is often better to use a named range.
• To assign a name to a range of cells, highlight it
using the mouse and choose Insert ►Name ►
Define and enter a name.
• Choose a useful name.
• Remember Excel does not distinguish between
the names PRICE, Price and price.
Entering a Matrix
• Choose a location for the matrix (or vector)
and enter the elements of the matrix.
• Highlight the cells of the matrix and
choose INSERT ► NAME ► DEFINE.
• Enter a name for the matrix.
• You can now use the name of the matrix in
formulae.
Addition, Subtraction and Scalar
Multiplication Etc.
To add two named 3 x 2 matrices A and B:
• Highlight a blank 3 x 2 results area in the
spreadsheet. (If the results area is too small, you
will get the wrong answer.)
• Type =A+B in the formula bar and press the
CTRL, SHIFT and ENTER keys simultaneously.
• You must use the CTRL, SHIFT,ENTER keys if
you want to perform a matrix computation. (If
you don’t do this, you will get an error message
or the wrong answer.)
Addition, Subtraction and Scalar
Multiplication Etc. (Cont’d)
• If you click on any cell in the result, the
formula {=A+B} will be displayed. In Excel,
the { } brackets indicate a matrix (array)
command.
• For an example of scalar multiplication,
see the Example Spreadsheet on the web
page.
Matrix Transpose
• Suppose A is a 3 x 2 matrix.
• The transpose of A, A’, will be 2 x 3.
• Select a 2 x 3 results area, type
=TRANSPOSE(A) in the formula bar and
press CTRL, SHIFT, ENTER.
• Exercise: Choose A and B so that AB
exists. Check that (AB)' = B 'A‘ using
MMULT (matrix multiplication).
• What do you think (ABC)' is equal to?
Matrix Multiplication
• Suppose A and B are named 3 x 2 and 2 x 3
matrices.
• Then AB is 3 x 3 and BA is 2 x 2. This illustrates
the fact that, in general, AB is not equal to BA,
even if the matrices are conformable.
• Select a blank 3 x 3 area for the result AB.
• Type =MMULT(A,B) in the formula bar and press
CTRL, SHIFT, ENTER to generate AB.
Matrix Inverse
• Suppose B is a square 2 x2 matrix.
• Select a 2 x 2 area for the inverse of B.
• Type =MINVERSE(B) in the formula bar and
press CRTL, SHIFT, ENTER.
• If B is singular (non-invertible), you will get an
error message.
• Suppose A and B have the same dimension and
are both invertible. Show that (AB)-1 = B-1A-1.
• What do you think (ABC)-1 is equal to?
Matrix Determinant
• Suppose A is a square matrix.
• The determinant of A, det(A) or IAI, is a scalar.
• Select a single cell, type = MDETERM(A) in the
formula area and press CTRL, SHIFT, ENTER
(or just ENTER).
• If A is singular, then det(A) = 0.
• Exercise: Check that det(AB) = det(BA) =
det(A).det(B), where A and B are square
matrices.